We now define a specific kernel that is the main object of our study. Let \(\Psi \colon \mathbb {H}\rightarrow \mathbb {R}\) ,
\(\Psi (v)=\Vert v\Vert _\mathrm {Kor}^{-2}\) . By a celebrated result of Folland, see [1]} and [2]}, we know that the fundamental solution of the sub-Laplacian equation
\(X_\mathsf {L}^2+Y_\mathsf {L}^2=0,\) 
